x(x+70)=350

Solution for x(x+70)=350 equation:

x(x+70)=350

We move all terms to the left:

x(x+70)-(350)=0

We multiply parentheses

x^2+70x-350=0

a = 1; b = 70; c = -350;
Δ = b2-4ac
Δ = 702-4·1·(-350)
Δ = 6300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6300}=\sqrt{900*7}=\sqrt{900}*\sqrt{7}=30\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-30\sqrt{7}}{2*1}=\frac{-70-30\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+30\sqrt{7}}{2*1}=\frac{-70+30\sqrt{7}}{2}
$